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Mathematical Methods and its Applications

Mathematical Methods and its Applications. Instructors: Dr. P. N. Agarwal and Dr. S. K. Gupta, Department of Mathematics, IIT Roorkee. This course is a basic course offered to students of Engineering/Science background. It contains ODE, PDE, Laplace transforms, z-transforms, Fourier series and Fourier transforms. It plays an important role for solving various engineering sciences problems. Therefore, it has tremendous applications in diverse fields in engineering sciences. (from nptel.ac.in)

Lecture 16 - Formulation of Partial Differential Equations

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Lecture 01 - Introduction to Linear Differential Equations

Lecture 02 - Linear Dependence, Independence and Wronskian of Functions

Lecture 03 - Solution of Second Order Homogenous Linear Differential Equations with Constant Coefficients I

Lecture 04 - Solution of Second Order Homogenous Linear Differential Equations with Constant Coefficients II

Lecture 05 - Method of Undetermined Coefficients

Lecture 06 - Methods for Finding Particular Integral for Second Order Linear Differential Equations with Constant Coefficients I

Lecture 07 - Methods for Finding Particular Integral for Second Order Linear Differential Equations with Constant Coefficients II

Lecture 08 - Methods for Finding Particular Integral for Second Order Linear Differential Equations with Constant Coefficients III

Lecture 09 - Cauchy-Euler Equation

Lecture 10 - Method of Reduction for Second Order Linear Differential Equations

Lecture 11 - Method of Variation of Parameters

Lecture 12 - Solution of Second Order Differential Equations by Changing Dependent Variable

Lecture 13 - Solution of Second Order Differential Equations by Changing Independent Variable

Lecture 14 - Solution of Higher Order Homogeneous Linear Differential Equations with Constant Coefficients

Lecture 15 - Methods for Finding Particular Integral for Higher Order Linear Differential Equations

Lecture 16 - Formulation of Partial Differential Equations

Lecture 17 - Solution of Lagrange Equation I

Lecture 18 - Solution of Lagrange Equation II

Lecture 19 - Solution of First Order Nonlinear Equations I

Lecture 20 - Solution of First Order Nonlinear Equations II

Lecture 21 - Solution of First Order Nonlinear Equations III

Lecture 22 - Solution of First Order Nonlinear Equations IV

Lecture 23 - Introduction to Laplace Transforms

Lecture 24 - Laplace Transforms of Some Standard Functions

Lecture 25 - Existence Theorem for Laplace Transforms

Lecture 26 - Properties of Laplace Transforms I

Lecture 27 - Properties of Laplace Transforms II

Lecture 28 - Properties of Laplace Transforms III

Lecture 29 - Properties of Laplace Transforms IV

Lecture 30 - Convolution Theorem for Laplace Transforms I

Lecture 31 - Convolution Theorem for Laplace Transforms II

Lecture 32 - Initial and Final Value Theorems for Laplace Transforms

Lecture 33 - Laplace Transforms of Periodic Functions

Lecture 34 - Laplace Transforms of Heaviside Unit Step Function

Lecture 35 - Laplace Transforms of Dirac Delta Functions

Lecture 36 - Applications of Laplace Transforms I

Lecture 37 - Applications of Laplace Transforms II

Lecture 38 - Applications of Laplace Transforms III

Lecture 39 - z-Transform and Inverse z-Transform of Elementary Functions

Lecture 40 - Properties of z-Transforms I

Lecture 41 - Properties of z-Transforms II

Lecture 42 - Initial and Final Value Theorem for z-Transforms

Lecture 43 - Convolution Theorem for z-Transforms

Lecture 44 - Convergence of z-Transform

Lecture 45 - Applications of z-Transforms I

Lecture 46 - Applications of z-Transforms II

Lecture 47 - Fourier Series and its Convergence I

Lecture 48 - Fourier Series and its Convergence II

Lecture 49 - Fourier Series of Even and Odd Functions

Lecture 50 - Fourier Half-range Series

Lecture 51 - Parseval's Identity

Lecture 52 - Complex Form of Fourier Series

Lecture 53 - Fourier Integrals

Lecture 54 - Fourier Sine and Cosine Integrals

Lecture 55 - Fourier Transforms

Lecture 56 - Fourier Sine and Cosine Transforms

Lecture 57 - Convolution Theorem for Fourier Transforms

Lecture 58 - Applications of Fourier Transforms to Boundary Value Problem I

Lecture 59 - Applications of Fourier Transforms to Boundary Value Problem II

Lecture 60 - Applications of Fourier Transforms to Boundary Value Problem III